It is true that PCA is based on assumption the data are normally distributed. Is your data daily, monthly or quarlerly data? Physio-chemical data are likely to be hourly or daily. Two year monthly data are just 24 in number, which is too small for a sample. The bigger the sample the better. The Central Limit theorem empowers us to use the normal distribution even where the normal distribution does not seem to apply especially when the sample is large. Non-normality may not pose a problem for that reason. Alternatively the data could be transformed to follow the normal distribution before PCA. The logarithmic or square root transformation is known to make data normally distributed.

No, it is NOT true that the basis of PCA uses an assumption that the data are normally distributed. PCA is based on the ideas of linear-relationships or linear combinations, and of variances and correlations. For real data-sets, the question is whether you are happy to restrict consideration to linear combinations of your original variables, where the importance of departures from any relationship is judged equally across the whole range of the data-set (were the meaning of this last changes depending whether you apply PCA to the original variables or to scaled versions, possibly doing a PCA on a correlation matrix). Using a pre-selected set of transformations to individual original variables might overcome some problems of apparent non-linearity and changes in variability, but this cannot treat all possible scenarios. A starting point is to understand both what PCA was devised to do, and what you are trying to do with your data-set ... there is no point in putting a lot of work into PCA if it is not suited to your purpose.

I have to admit that some formal parts of PCA are based on an assumption of full multivariate normality, such as results for the distribution of eigenvalues, so you need to be cautious of such results. Also, an attempt to choose transformations to overcome non-linearity and variability problems can lead to the transformed data-set looking "more normal" in some sense.

Simply NO

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The data needs not be normally distributed but linear to use PCA.